3 points one circle
2010-01-23 8:42 pm
How to prove analytically (by using coordinate geometry only) that there is one and ONLY one circle passing through three non-collinear points? Thanks.
回答 (3)
2010-01-23 10:28 pm
✔ 最佳答案
Have to show the 3 simultaneous equations have unique solution...2010-01-23 14:28:46 補充：
Please see the analysis below :
圖片參考：http://img51.imageshack.us/img51/4213/uniquecircle.png
2010-01-23 14:28:54 補充：
http://img51.imageshack.us/img51/4213/uniquecircle.png
2010-02-02 6:19 am
哈哈 , 其實有讀AL 都明個 PROOF ,
不過要過程100% 岩都有D 難 , 錦多ABCD ,
好易迷失 XD
不過要過程100% 岩都有D 難 , 錦多ABCD ,
好易迷失 XD
2010-01-23 10:03 pm
The standard equation of a circle is given by :
x^2 + y^2 + Dx + Ey + F = 0 ; (D^2 + E^2 - 4F) > 0
There are three unknown D , E , and F.
We can set up three equations to solve D , E , F (have and only have one set solution for 3 equations and 3 unknown) if we known any 3 non-collinear points.
2010-01-23 14:04:27 補充：
I don"t know how to show the 3 simultaneous equations have unique solution.
x^2 + y^2 + Dx + Ey + F = 0 ; (D^2 + E^2 - 4F) > 0
There are three unknown D , E , and F.
We can set up three equations to solve D , E , F (have and only have one set solution for 3 equations and 3 unknown) if we known any 3 non-collinear points.
2010-01-23 14:04:27 補充：
I don"t know how to show the 3 simultaneous equations have unique solution.
收錄日期: 2021-04-21 22:14:58
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https://hk.answers.yahoo.com/question/index?qid=20100123000051KK00588